Part I. We analyze how a decaying cavity field can lead to significant atomic cooling. This cooling can be intuitively understood by invoking the adiabatic theorem to characterize the dynamics of an atom dressed by a classical field. We find numerically that cooling can proceed well into the quantum regime where there are only a few photons left in the cavity, and where the adiabatic theorem ceases to be applicable. A physical interpretation of this final cooling stage is given. Part II. We evaluate a nonlinear atomic homodyne detection scheme for measuring the Wigner characteristic function of a microwave cavity field. We find numerically that the semiclassical approximation, on which this scheme is based, does not give results consistent with a full quantum calculation. We analyze the back-action of the measurements on steady-state 'macroscopic superpositions' that can be generated in high-Q microwave cavities. We show that the measurements required for a full characterization of the state destroys the macroscopic superposition such that it cannot be reconstructed by using the scheme that was used to generate it in the first place.
We present a scheme for a compact rubidium cold-atom clock which performs diffuse light cooling, microwave interrogation, and detection of the clock signal in a cylindrical microwave cavity. The diffuse light is produced by laser light reflection at the inner surface of the microwave cavity. The pattern of the injected laser beams is specially designed to accumulate the majority of the cold atoms in the center of the microwave cavity. Microwave interrogation of the cold atoms in the cavity leads to Ramsey fringes, which have a linewidth of
24.5 Hz with a contrast of
95.6 when the free evolution time is 20 ms. Recently, a frequency stability of $7.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}\phantom{\rule{0.28em}{0ex}}{\ensuremath{\tau}}^{\ensuremath{-}1/2}$ has been achieved. The scheme of this physical package can largely reduce the cold-atom clock complexity and increase clock performance.